$A$ bomb of mass $16 \,kg$ explodes into two pieces of masses $4 \,kg$ and $12 \,kg$. The velocity of the $12 \,kg$ mass is $4 \,ms^{-1}$. The kinetic energy of the second piece (the $4 \,kg$ piece) is: (in $\,J$)

$A$ projectile of mass $m$ is projected from ground with a speed of $50 \, m/s$ at an angle of $53^{\circ}$ with the horizontal. It breaks up into two equal parts at the highest point of the trajectory. One particle comes to rest immediately after the explosion. The distance between the pieces of the projectile when they reach the ground is: (in $, m$)

$A$ shell at rest at the origin explodes into three fragments of masses $1 \ kg$,$2 \ kg$,and $m \ kg$. The $1 \ kg$ and $2 \ kg$ pieces fly off with speeds of $5 \ m/s$ along the $x$-axis and $6 \ m/s$ along the $y$-axis,respectively. If the $m \ kg$ piece flies off with a speed of $6.5 \ m/s$,the total mass of the shell must be ......... $kg$.

An artillery piece of mass $M_1$ fires a shell of mass $M_2$ horizontally. Instantaneously after the firing,the ratio of kinetic energy of the artillery and that of the shell is:

$A$ particle of mass $m$ is moving along the $x$-axis with a speed $v_0$. Suddenly,a part of its mass,$m/3$,breaks off and moves parallel to the $y$-axis with a speed $2v_0$. Find the velocity of the remaining part in terms of unit vectors.

An open water-tight railway wagon of mass $5 \times 10^3 \text{ kg}$ coasts at an initial velocity $1.2 \text{ m/s}$ without friction on a railway track. Rain drops fall vertically downwards into the wagon. The velocity of the wagon after it has collected $10^3 \text{ kg}$ of water will be .............. $\text{m/s}$.